I would like to include the SE image flair on my website. However, for various reasons (mostly privacy, some legal uncertainties), I would prefer if this image was included locally, rather than causing a request to the SE servers each time someone visits my website.

That is, I would get a cron job to download http://stackexchange.com/users/flair/1912106.png every few days, put it in a some directory on my server and then use

2 Answers
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This would not violate any trademarks. The only thing on that image which actually belongs to them is the site logo (or logos if it's the combined flair). So as long as you're linked back to your profile like a normal flair image, there's absolutely nothing wrong with downloading and hosting it yourself. Everything else on there is just text, some colored circles, and your Gravatar; it's not like they can "own" that information.